Does natural shampoo make your hair oily a lot faster than normal shampoo?

So I used pureology before but I wanted to use natural shampoo so I can stop using toxic ingredients that cause cancer so I just want to be healthier

But I noticed my hair gets oily a lot faster! I have color treated hair so idk if that matters but my hair never gets oily literally like 2-3 days after washing my hair with regular shampoo but since I used natural shampoo my hair got oily so much faster

Is this normal?